Parametrized Homology via Zigzag Persistence
Algebraic Topology
2019-03-20 v3
Abstract
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding to a homological feature supported over that interval or, equivalently, as a persistence diagram. By defining persistence in terms of finite rectangle measures, we classify barcode intervals into four classes. Each of these conveys how the homological features perish at both ends of the interval over which they are defined.
Cite
@article{arxiv.1604.03596,
title = {Parametrized Homology via Zigzag Persistence},
author = {Gunnar Carlsson and Vin de Silva and Sara Kalisnik and Dmitriy Morozov},
journal= {arXiv preprint arXiv:1604.03596},
year = {2019}
}